Adsorption of carbon dioxide in the metal− organic framework CPO-27-Mg (Mg-MOF-74) is examined. We use accurate quantum chemical ab initio methods (wave function-type electron correlation methods for cluster models combined with density functional theory for periodic systems) to calculate gas−surface site and gas−gas interactions. At 298 K, the "zero-coverage" enthalpy and Gibbs free energy of CO 2 adsorption on Mg 2+ sites are −46 and −9 kJ/mol, respectively; for linker sites these values are −30 and +5 kJ/mol, respectively. For full monolayer coverage lateral interactions from nearby molecules contribute −6 and −5 kJ/mol to the adsorption enthalpy for CO 2 at Mg 2+ and linker sites, respectively. The predicted heats of adsorption and free energies of adsorption agree within 2.6 and 0.8 kJ/mol, respectively, with experimental values well within chemical accuracy limits (4.2 kJ/mol). We use two different ways of calculating isotherms from equilibrium constants for individual sites and interaction energies: (i) a Langmuir model, augmented with the mean-field (MF) approximation for lateral interactions, and (ii) grand canonical Monte Carlo (GCMC) simulations on a lattice of sites, which agree very well with each other. We use GCMC data to examine how different isotherm models (Langmuir, dual-site Langmuir, Sips, Toth, and mean-field) fit them. We conclude that the MF model yields the best fit over a wide pressure range with physically meaningful parameters, i.e., adsorption constants for individual sites and lateral interaction energies.

For CO and N on Mg sites of the metal-organic framework CPO-27-Mg (Mg-MOF-74), ab initio calculations of Gibbs free energies of adsorption have been performed. Combined with the Bragg-Williams/Langmuir model and taking into account the experimental site availability (76.5%), we obtained adsorption isotherms in close agreement with those in experiment. The remaining deviations in the Gibbs free energy (about 1 kJ/mol) are significantly smaller than the "chemical accuracy" limit of about 4 kJ/mol. The presented approach uses (i) a DFT dispersion method (PBE+D2) to optimize the structure and to calculate anharmonic frequencies for vibrational partition functions and (ii) a "hybrid MP2:(PBE+D2)+ΔCCSD(T)" method to determine electronic energies. With the achieved accuracy (estimated uncertainty ±1.4 kJ/mol), the ab initio energies become useful benchmarks for assessing different DFT + dispersion methods (PBE+D2, B3LYP+D*, and vdW-D2), whereas the ab initio heats, entropies, and Gibbs free energies of adsorption are used to assess the reliability of experimental values derived from fitting isotherms or from variable-temperature IR studies.

Gibbs free energies of adsorption on individual sites and the lateral (adsorbate-adsorbate) interaction energies are obtained from quantum chemical ab initio methods and molecular statistics. They define a Grand Canonical Monte Carlo (GCMC) Hamiltonian for simulations of gas mixtures on a lattice of adsorption sites. Coadsorption of CO and CH at Mg sites in the pores of the metal-organic framework CPO-27-Mg (Mg-MOF-74) is studied as an example. Simulations with different approximations as made in widely used coadsorption models such as the ideal adsorbed solution theory (IAST) show their limitations in describing adsorption selectivities for binary mixtures.

We investigate the prototypical NAI-DMAC thermally activated delayed fluorescence (TADF) emitter in the dilute- and high-packing fraction limits at finite temperature, by combining first principles molecular dynamics with a quantum...

A new mixing rule (geometric mean) is proposed with substantial improvements compared to the widely used ideal adsorbed solution theory for adsorbates with strong lateral interactions.